{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## General Mixture Models"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "author: Jacob Schreiber <br>\n",
    "contact: jmschreiber91@gmail.com"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is frequently the case that the data you have is not explained by a single underlying distribution. Typically this is because there are multiple phenomena occuring in the data set, each with their own underlying distribution.  If we want to try to recover the underlying distributions, we need to have a model which has multiple components. An example could be sensor readings where the majority of the time a sensor shows no signal, but sometimes it detects some phenomena. Modeling both phenomena as a single distribution would be silly because the readings would come from two distinct phenomena.\n",
    "\n",
    "A solution to the problem of having more than one single underlying distribution is to use a mixture of distributions instead of a single distribution, commonly called a mixture model. This type of compositional model builds a more complex probability distribution from a set of simpler ones. A common type, called a Gaussian Mixture Model, is composed of Gaussian distributions, but mathematically there is no need for these distributions to all be Gaussian. In fact, there is no need for these distributions to be simple probability distributions.\n",
    "\n",
    "In this tutorial we'll explore how to do mixture modeling in pomegranate, compare against scikit-learn's implementation of Gaussian mixture models, and explore more complex types of mixture modeling that one can do with probabilistic modeling."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sat Oct 06 2018 \n",
      "\n",
      "numpy 1.14.2\n",
      "scipy 1.0.0\n",
      "pomegranate 0.10.0\n",
      "\n",
      "compiler   : GCC 7.2.0\n",
      "system     : Linux\n",
      "release    : 4.15.0-34-generic\n",
      "machine    : x86_64\n",
      "processor  : x86_64\n",
      "CPU cores  : 4\n",
      "interpreter: 64bit\n"
     ]
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn; seaborn.set_style('whitegrid')\n",
    "import numpy\n",
    "\n",
    "from pomegranate import *\n",
    "\n",
    "numpy.random.seed(0)\n",
    "numpy.set_printoptions(suppress=True)\n",
    "\n",
    "%load_ext watermark\n",
    "%watermark -m -n -p numpy,scipy,pomegranate"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### A simple example: Gaussian mixture models"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's start off with a simple example. Perhaps we have a data set like the one below, which is made up of not a single blob, but many blobs. It doesn't seem like any of the simple distributions that pomegranate has implemented can fully capture what's going on in the data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
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hYCWiwPi9sbvt6Tn9PD9BW+flM8Xi9ACQNAysRBSIsG/sbj/P6/CsbB5WNLQcpbg8ACQR\nk5eIKBBuNkaP0+fJ5mENQKsC9jqvn006BlYiCkTYN/agP8+s9yvrmRaAwB4avNB5/WzSMbASUSDC\nvrEH+XnFVaCsZAaz2vRaWVUpOgysRBQI2Y19+dUNk/uhrtt5XFkgCjKQOK0CBSCwCk5ucf1sdJi8\nRESBEGXeLr+6AS/3ZCaD1MmhMSUJTWY2cDaXR7VhIF8oIK1weYmb4eQoE4REWdFvdLSG3o5Kx8BK\nRIEpzbxdtrVbeaZqaTZwvlCY7KmqCm6yghIyUSQIcXmNPhwNBZ85cwbr16/HLbfcgltvvRW9vb1B\nt4uIEkhVgpGZSHR5Rxc2vXg48Gzg5Vc3CF+fOa18pxwgmgShsLOwSc5Rj/WJJ57A17/+dTz99NM4\nf/48RkZGgm4XESWQiv0/RT1UEZW9xr3HBoSvp6qrkKoaR278QhtSVUYkCUJcXqMP2x7ruXPn8NZb\nb+HOO+8EAEybNg0XXXRR4A0jPRT3DJZt7dYiKYOi5eecUJFg5DSRSGWvURacBrO5iQWsxUr/OyRc\nXqMPo1CQPO59pq+vD4888giuvPJKHDt2DIsXL8bDDz+Murq6yZ/p6emZ8t9RGxkZwYwZM6JuRiwV\nH7vu/rN4ev8nGC3aXHp6tYH1X/s8WhfOjqqJWqqUc07FOdHdfxbbD57CwNAYPl9Xjf+xdK6r8+kb\n2/thedPy0CY763Yex8mhsbLXqwxgXNCYeTNrsP3OS119RvFxaZhZg3XXzbFsf+k5x+vVGVXX6vDw\nMJYuXSr8N9vAeuTIEaxduxb/9E//hCVLluDxxx/HrFmzcP/990/+TE9Pj/QDotDX14empqaomxFL\nxcdOthg+XV/LTMMSlXLOqT4nvBw3WRuqDQPjhUIgxeZLh5+BiZ62rOdsAHh36ypf729gouiELLtZ\ndOxYdN+eqmvVKu7ZzrE2NjaisbERS5YsAQDccssteOaZZ3w3ivTHORsqpcM5IduZZs3SNPYeG8CH\ng9nJhB1VQUVWtH/b6+/4njM237c0SJs9nsxgFu0vHcZjrx2dsl3eIkGni9vT6cE2sDY0NKCxsRH9\n/f1YuHAh3nzzTVxxxRVhtI0ipiLRhJJFh3PCyfpYp0tN3PTwZEHL6/ZzxeweTHLjBZwazgG4EGjv\nX/Z5VMAgSSw5Wm7zyCOP4IEHHsDtt9+Ovr4+3HfffUG3izTAkmhUSpdzoq0ljTc6WvHu1lV4o6MV\ne48NuF5qUlymsIALwdhNMpaq6kZuH0xy4wX839994up3KDyOlts0NTXhlVdeCbotpJkgN5qmeNL1\nnPAyRK1qWzUVw6+i4W07Z8/bpXBRVFh5iSxxzoZK6XhOeBmi1mG+2FT8wJIZzE4mLlE8MbASUezJ\nEpqshqh1mC8uVvzAUjz3CwMQrd24aLq3PVSYORw87m5DRLHnZa5Tl/likeI55Ke+fS1S1VOrTqSq\nDfzwq59z/b4q5pXJHnusRJQIboaog94NRyXZvPaiGWdcv5eqeWWyxsBKRBUljN1wVBM9NPT1uQ+s\nOs0rJxmHgomoolTyLjCsJxwOBlYiqiiV3GvTeV45STgUTEQVJcps4KgzcnVdh5w0DKxEVFG8LM1R\noXRu12nZRdXCWocc9UNElDgUTEQVRVUZQrcqaW630pf1sMdKRBUniupRlTS3W+nLethjJSIKQSVl\n5FbSQ4QIAysRUQgqKSO3kh4iRBhYiYhCENXcbhQq6SFChHOspEQlZwASOaXjzkBBqPRlPQys5Jsu\nywiISB+V8hAhwqFg8q2SlhEQEdlhYCXfKj0DkIioGAMr+VbpGYBERMU4x0q+RVUijojITmli5d3N\ns9DUFOxnMrCSb5WeAUhEehIlVj69fwTpBZlA708MrKREJWcA+sWlSkTBECVWjuYLgZdWZGAlihCX\nKhEFJ6rESiYvEUWIS5WIghNVYiUDq0edvRks29qNyzu6sGxrd8Vsh0RqcakSUXBEpRWnVxuBJ1Zy\nKNgDDt+RKgvqa5ERBFEuVSLyT5RYeXfzrMDv0wysHsR9r0G3yTJMrgkOlyoRBas0sbKvry/wz2Rg\n9SDOw3due9vsnQeLS5WIkoeB1YM4D9+57W3HvXceB1yqRJQsTF7yIM57Dbrtbce5d05EFAX2WD3Q\nefjObj7UbW87zr1zIqIoMLB6pOPwnZP5ULfJMsuvbsCvDxxHoei1uPTOiYiiwKHgBHFSbKCtJY0t\nq5uRrq+FASBdX4stq5uliUsv92SmBFUDwJql+j1UEBHpgj3WBHE6H+q0ty0K1AUAe48NTHmNy3GI\niC5gjzVBVJfvchKozeHnzGAWBVwYfmYlKiKqVAysCaI6W9lJoGatWyKiqRhYI6S63rCb+VMnnARq\nLschIpqKc6yKeCkTGERFI5XZyk6WFXE5DhHRVAysCngJknGpaGQXqFnrlohoKg4FK+BlnjEpQ6iq\nh5+JiOKOPVYFvARJP0Ooui1v0bFYBhFRVNhjVcDLMhevGbxc3kJEpDcGVgW8BEmvQ6hc3kJEpDcO\nBSvgtSi/lyFUXeZmdRuOJiLSBQOrhNvAEdY8ow7LW+yyoBl0iaiSMbAKBLXGVAWr5S1hBTS74Whd\njx0RURg4xyqg8zymbG4WQGhJTVbD0aqPnerqVEREQWOPVUCXeUwZ0bDzsq3doRWcsBqOVnnsdB45\nICKSYY9VQPUuMWEI82HAKgta5bHTeeSAxDjCQMTAKqR6l5gwyAJXAVB+g7NaKqTy2Ok+ckBThbXG\nmsGbdMfAKhDHMn2igGYKs4iEymMXx5GDShbGCAMLpFAcOJ5jzefzWLNmDebPn49f/epXQbZJC3Er\n01e8llY0/6lyvtVu7lPVsWOB/3gJY4QhLptXUGVz3GN9/vnnccUVVwTZlkSIcpiqrSWNNzpaYUj+\nXdUNLqy5zziOHFSyMEYYOD1AceCox/rxxx/jt7/9Le677z4899xzATcpvnQpnBB0EYkwb25xGzmo\nZGGMMOhQICUpWMglOI4C65NPPon29nYMDQ0F3Z5Y81o4wfxdVSd40Dc4u5ubmwuWF3dyeC3t6Qan\nB9TgUrZgGYVCoWD1A3v37sW//du/YfPmzfjd736Hf/iHfyibY+3p6UFdXV2gDXWqu/8snuv5FJ8M\n59EwswbrrpuD1oWzQ/nsb2zvh+hgGgAaZtbg5NBY2b/NnmbgfB4YzV/4zenVBtZ/7fOe293dfxa/\n+v2fcWZ0fPIz7rte/H7d/Wex/eApDAyNoWFmDe5unoWVi+bavv/T+z+Z0ubi75MdK2Bs/MJr06sN\n/LcrZ+GtD7I4OTSGKgMYLwAXTa/C0PlxFL+N3+8elZGREcyYMSPqZsSOl+NWes6GeY3rxM85t27n\nceH9aN7MGmy/81K/TdOaqmt1eHgYS5cuFf6bbY/14MGD6O7uxr59+zA6Oopz587hgQcewM9+9rMp\nP9fU1OS7oX519mbwywPvTT6FnRwawy8PfIr0grDq+H7kunDC2fPlwWk0X8ALR87hR6u+6roNF47B\nhcg2VqhCekEaTU1pyc9eOF7/563T+NJlX7I8Xk1NQHpBZjJRygAmHyhk36frnbOT/z3+2Y+Ygb/0\nZ71+d/M7RdED7uvr0+IaiBsvx62pCfjRqoAaFCN+zrmBoX7J62OJP49VXas9PT3Sf7NNXtq0aRP2\n7duH7u5u/PznP8cNN9xQFlR1EXVBAS+FE2S8zle6OQainx3NFxwdLzNRKl1fK+yl++H0u5cmiv2v\nziNcikHkAJeyBStR61ijzhj0UjhhTl1K+F5eT3A3x0DF8Qri2FYZhm0w7OzNoH3n4SlB9B8PHGel\nJiIH4lgEJ05c1Qq+/vrrcf311wfVFt90yBiUZbHKEjsAKE3GcHMMZD9bLwn2bj7Pj3yhYJtI8dhr\nR5ETzPGKcCkG0VRhJJpVskQV4dc9Y9Bq6YiqE9zNMWhfuQjtOw+XBahzI2Po7M04aoPo84rNqUth\nNJfHcK58PtVKNpfHphcPY8OOQ8Jjcmo45/i9OLxFVI5L2YKTqMBqniRP7v5PDAyNhfYU5jdhRuUJ\n7uZJtK0ljc2vHsVgdmqQyo0XHFeyMX9m04uHkRckmNdNq8FPbl+M9pcOIzfubjbWfD8/SwF0erDi\n0iKK6hzguReuRAVWYOLGu2jGmdAy26JaD2Z1obgJ1Kez4p6fm+HTtpY0Nuw4JH0fUbAfGh0rC+hW\nSsvW1demhL9fl6rCnJnTtbuBcN0gRXmv4LkXrsQF1rBFUbvUTNwxh3Azg1m07zwMwP2Fompe2u59\nSoN96XdwojjYb/5meS84VWXgydX/VcubBWvcRkOnnlpU5wDPvfAlIiu4dNlFd/9Z+19SJIpMZFHi\nTi5fwGOvHXX9XqqyA92+T1tLGjOnuXuuKw72bS1pbLtryZQM7G13LQnkRqGi/nPUGeuVSLedcKI6\nB3juhS/2PVbRMMfT+0eQXuAs+cavKDKRZYk7bhJ6TKXDtA0za/DQbde4PnZesgxlw9DARFC2S8AK\nI/lC1TCaDhnrlUa3nlpU5wDPvfDFvsfqp8iBCklYD2YWe3h36ypsv/NSzzed4vd5o6PV9n1kF7a5\n/leHXW1UFR1JwnkSN7r11KI6B3juhS/2PdaoL54o1oPJEnfqa52vP9WB1dIgXZYCqDq/uG6wXGdv\nBk/uPo6Bof5AjoduPbWozgGee+GLfWDV4eLxGwTcJljIEnc2f3Ox5zZEweqC1yXpROX5pcvDgg7C\nyFTVcV17VOcAz71wxT6wii6e6dVGbIY5/lfnEfz6wPHJertObjAqn0BLA9jdzbMQZg1u0QUfxE3X\na6DW8eacBGHMf6q6TnR5yKP4iH1gFV08dzfPisWJ39mbmRJUTU5uMCqeQFUnfqm6Aam+6foJ1BxG\nC0ZYUzgqRpO4BpTcin1gBcovnr6+vghb49y219+R7gzj9QbjJrhZJX55eapXdQNSfdP1G6g5jKae\nDlM4TuiWWUzxEPus4DizChQL6mtdr590u25PZQBTuWWf6i2tZJsEcB1fdOKSqRp1ciTFEwNrhGSB\nwgCw/OoG14vb3QY3lQFM5Q1I5U23szcDQ/JvbnbxIbXMLRbnzayJfEmVFe5bSl4wsEZIFEAMAN+9\n4VLsPTbgugfoNriJPt9r4pfKG5DVvrZuWQ23m7v4UDTaWtLYfueljtc9q+ZkRCguPWvSSyLmWL3Q\nIdPPKjHm8o4u4e/YDR+7mbfyk/hVevyWX92Al3syjrJnnRx7VfOaVsfLzS4+TulwXsVNFMfMaU4A\nk9fIi4oMrDpl+skCiJfkDi9LQ7wkfomO38s9GaxZmsbeYwP4cDCLi2tTMAxgw45D2Pb6O1PWpwZ9\n7Itv1FWGIdzOzqRyrkyn8youuvvP4pcH3gv9mLlJSmLyGrlVkUPBKhNtVDOHpzKD2bK5QSdBMoxS\ngLLjt/fYAN7oaMVTa6/F6Ng4Tg3nJueHN+w4hC91dGHTi4ddHXu/CVxWQRVQO1em83mlq+0HT0Vy\nzJiUREGqyB5rFBeVk+Gu0h5PARNzrgVMBEknQ1BhPF3bHT9RgDHDmyzQid7TSw9Q9NkAUGUApfus\nq54r483avYGhMeHrQR+zuCz3oXiqyMAa9kXlNEDIAlK6vhZvdLTafkZY80B2x8/LTfHi2hSWbe2e\n0n4vawhln10oAL9Ye22gx4g3a/caZtbgpCC4Bn3MdKmoxTn5ZKrIoeCwM/2cDhF67fGEve+k3fFz\ne1NMVRkYOj9W1n4v60+tspPd7r7jFjNIp3IyjL/uujmRHLOwpk2s6LZfLKlTkT1WP5l+bp8wO3sz\njgOE1x5P2NVh7I6fqDcgU/9ZklPpXrLZXB7VksQj1QlcqjCD9AKnozStC2cjvSAdyTGLOimJVZ2S\nqyICqywYBl22z/x5mdIA4TUo+Jnb81qE3+r4FQcYMwlLlkI0OjYuDcD5QsHRhuel36O+LoXpNVU4\nnc2FHtyivlnrglm39jgnn1yJD6wql0C4fcKUJdIA4gDhtcfjtaerugh/seKbZekOPsWseqbporlW\nN0lfp4ZzqE1V46m114a+Gw5N0CFo6P435Jx8ciU+sD722lFlwy1ubxZWNxHZfI6Xp3evPV2VRfit\n7D02IO2xAtY9UyfHQ6fdcJLKbZByEjSC3Og8Dn9DXRKoSL1EJy919mbK5u5MXp6cZU+SBUCYnCH7\n+fRniTSqeE3EkB2DzGDW1drogY+YAAAc8ElEQVRRO3bH2myv10QSlb2jzt6M67W2SeclycYukct8\nz5NDY4Ek7sRhTbEOCVQUjET3WK0uIi/DLe0rF6F952Hk8uX9L9ETcVBPpKrmjGW9CgMXdoRR8aQv\n+xzAXc9U5uLaFAaz5Q9QF9e6K7Jv3uzdrLWtBF5GBOymNYJO3NFhKNqJ0vPezKTWcfha96F1nSQ6\nsFpdRF6CW1tLGptfPSq8iQPlN4Ygso9VDnHJsndFG69vevEwNuw45OmCkn2Ogam9CK8XqSHZvkb2\nuozVnDhQuXNfXoOU1cNS0IEvjvOXOg9f69w2HSU6sMourvralOeT4bQkqJpKbwyqs49VPumLAr+s\nZ2n24kQXlN2TbGmWsFkFyQzgbi5S0WcNSob7Za/LWN3UK3nuK4ggFXTg03H+0u460Xn5jc5t01Gi\nA6vs4tr8zcWe39Mq+Jj/7pfVSaz6Sb808H/1f78urIRT2pbNrx4VLqex2yVEtr7VyUUqe+Cor0sJ\n59Ld/i1kf9tqw/A99xXnYbQggpTsPZdf3aBkKFS3NcVOenyy+4rV/SYscRla10WiA2sQF5dV8YPS\n5Ayvn2t1Evt90rdr17rr5uCXBz61Le4wmM1NDomLho5FQdJuqNXuIpU9cEyvqXK83tWK7GavIqjG\neRgtiOvI/N0nd/8nBobGhFsP+j1OOq2PddLjky07q3Y7pxGAMIfW4/wQakp0YAXUX1ylw5rmxZBW\nMA9qnlCypSnmSea19+CkXaWVcKz3hpETBUm7wGl3kcp+/3Q2h6cU1AEOqpeThGG0IIJUW0sai2ac\nQdNnFUmWbe2O/XGSscrAv7yjCwvqa6VJc/lCAcu2dkcaYGQdiuHzY+js9b/u3RT3h1BT4gNrEOxu\nMl5upKUnVKni7FnzM9ze/GXteuiVt7HpxcPIFwqoMoC7r790suj/lyQbrtsRBUkn2cF27yl7avZ7\n4y99Sn5q7bUAJo6Z16QtE4fRnInqOIXRQ7I6983lRlYVyqIOMOZnliZvnhrOKW1XEh5CgYSvY42K\nlxuE1TBp6fq2thZvxeRlF/ZwbnzyaXm8APzjgeP4L4/8Bp29GaQ9DPXIgqRobSMwkUzmZLg1qCL3\nonWa7S8dRvvOw0oKpFttDEAXRHGcwiqELzv3i5nbRMpEvQ63rSWNmdPL+2Iq25WUh1AG1gB4uUHI\nThwDULITS2dvxvKiLTWcG8eDrxzB8qsbbG8IxayCpGhB/C/WXotDP1nh6PsFtaBe9FCTGy+UrVf2\negPhrjfORHGcwiokUXruypjbRMpEHWDCWCbl5nVdcSg4AF7mQVVltspYzd3KZHN57D02gC2rmx3P\nuY6OjVv+u98h2yDm+tzcFLzcQHTLUNWV3+PkZUg3zB5S8bm7bGu3cATJ3HtZ9u9RB5hKXCblBQNr\nANzeIDp7Mzg3Ur7EJVVt2O7k4vcGYufDwayjG4IpjvMhdkuoSn/WC50yVHXm9Th5TXqJqpCEXQDR\nNcAE3a6kPIQysAbEzQ1i2+vvIDde3hecOa2m7D1U30DsONnarlTUw1Vuib5TqsoADEwZDtbhxlaJ\nnDxIek16iSqA2QUQXQNMGO1KwkMoA6tiTnuTxT8nG14VVXlSeQOxY6C89GPpciORqIer3JLdLESv\nxf2CjxunD5J+yi4C0fyd7QKIrgFG13bpROvAGreFwqKbwIYdh/Af732Kx9uapT8nIwpQKm4gpetv\nrZYByJKQROt1gfj26mQ3C53Pt0rg9EHSz5BunAJFZ28Gj712dDIfo772fWz+5uLYtL9SaBtYg14o\nHETQFt0ECgB+feA4vnLZ3CnBzS6oygJUEDcQq0QKu/cD/D3tx+3hicLl9EFS1zlJlTp7M2W7aw1m\nc2h/6TAAPgTqRNvAGuRC4aCCtuwmUACmtNuqd2kAlgHGb+UlURDz855+nvZlPfz7dxyaUsmKpqqk\nhxGnD5K6zkmqtO31d4RbVubGC77ui5V0PoVF28AaZBp8UEHbKkGouN2yn5tTl0LvoyssP8PrDcTJ\nw0TYF5eshy9rHyWn5JtTbh76whzSjSIYWd37vN4XK+18Cou2gTWINHjzYnAS/LxoX7kIG3YcEiYj\nFbdbtmH6uRFndTe93EDsHibM//X19U3Wbg2a3fGO49KdoCWl5JtTOvZE/dYC9/o9rB7cvd4XK+18\nCou2gVX1nImThCG/2axtLWn8x3uf4tcHjk8JrqXtbmsRb5jud0jHShSlwuxuJE6WAAXVvrgOf+le\n8i2I46pbcpGKWuBue4advRkMjYq3c0xVide7O6H7+RRX2pY0VF2+zi5hSFWiw+NtzXhq7bW27ZZt\nmB7UCR12qTAnNVid1E8NaluqMOrDBkGHkm+dvRks29qNyzu6sGxr9+Rxi+NxlX0XK6pqgTstnWge\n19IHcWCihOi2u5Z4vi/qcD4lkbY9VsD+SdXN07HVSa86UcbJE3bYFV/Czpp08lRfugSodHePoNoX\n5+GvqLNfrXpeTo9r8XXbMLMGD912USTHPcxqTVbbxtltCSfrFMybWYPfP2Kdk2En6vMpqbQOrFas\nLopFM8p/XnYxmLU5wxb2CR32XJXTp/rihxAvxTW8fI84D39FPedoFTydHNfS6/bk0FhkyTJhVmuy\nmvawC+iy4zowJB4adiPq8ympYhtYrS6KZ+/4QtnP6/ZkFsUJHeZclZeneiftU5HFGFV9WFWinHO0\nCp5OjqtOowVhVmuyq3xmdQxkx7Vhpprbt25z2EkQ28BqNbTS3X8WpYmtOj6ZuTmh45ZsE9SDjIob\ns24PWaoFea5YBU8nx1Wn0YIwqzWVTnuIyI6B7Liuu26O48+ncMU2sFoNrTy9/xOkF5QvW4nrk5ku\na83c3LCDepBRcWPW8SFLlaDPFavg6eS46jRaEMV0TFtL2vWWcLLjumjGmUDaSf7ZBtaPPvoIf/d3\nf4dPPvkEVVVV+Pa3v41169YF1iCnN2+roZXRfHDLVqKgw/CZ1Q3bbGPp3yyIBxlVN+a4PmTZCfpc\nsQuedsdVp9GCqB6wRMfAgHUik+i49vUxsOrKNrBWV1ejo6MDixcvxrlz57BmzRosW7YMV155pfLG\nuHnaNv/7/h2HhO8Vh0QUp3QYPpPdsDe/ehSjY+Oh9aZ1ujHrKIxzxc9Difl7xeu4q4yJ/96w41Do\nowdRPGBZZcOz8lEy2K5jnTdvHhYvXgwAmDVrFhYuXIgTJ04E0hi3a73aWtLSQvFxSURxIoi1ZqL1\ne529GazbeVy4pk92Yx7M5jyvz/NC9frmpInLusTRsfHJ/z90Po/BbE669tXLWlPdtbWk8UZHK9L1\ntWWV2oK8figcruZYP/jgA/T19WHJkiWBNMbL07aoBzO92nslEh0FXYUqM5hF+87DQAGTG66XPjm7\n3Sjdbw/JakrATy8jbklgbsWhR29XrKV46FqX/IKg6DAaReoZhUJBts/2FENDQ/je976H++67DytW\nTF2U3NPTg7q6Ot+NWbfzOE4K1mbNm1mD7XdeKv297v6z2H7wFAaGxtAwswZ3N8/CykVzLX9m3XVz\n0Lpwtu82h0Vl+2XHWcQ89t39Z/H0/k8wWlTfeHq1gek1Bs6Mjkt/zwvZZ63/2ud9/c2Cel8AGBkZ\nwYwZggXUEdD9XP/G9n5hPe1iBoD/t26h53tCWPwea7vvZ/X+Op1zcaLquA0PD2Pp0qXCf3MUWHO5\nHO677z7cdNNNuOeee8r+vaenR/oBbsg2znY71FdaSF7V+ybF5R1dtje2YmZlKqA80QOA8mNrtT+s\nn2IeQb0vUH7OkZzs71DM/JtYnat2WywGze99pXTT8tL3AKyvLZ5z3qg6blZxz3YouFAo4OGHH8bC\nhQuFQVWloLL0dMiq1YnbYV1z+G3L6mZpADITMaoNY8ockZfjG9TwGIfd9GBXLKF46NrqXC2ekwX8\nDw27nSbwUsLR6oEUmKj9u/mbiyeX5fC+FU+2gbWnpwe7du3CVVddhTvuuAMAsHHjRtx8882BNCiI\nLD2dbqg6zPGJbmypamPKHGspqwvafE3VXFhQax11WkNZyUofoOvrUigUJjamKL0m7IIwMHFubnrx\nsK+sYi9zuV5KOJrvO72mSvidZk6vmfw8ne5b5I5tYP3KV76Cd96Jd4aaLjdUXRIxZCMDAPDk7v+U\nzr963b3D7XcLKgEnDok9lcJ8gLYblis9V2XDwvmCOOnOqc2vHnV9/vop4Sh7UCi+xlTct3R4kK9E\nsa285IYuN1SdhqRlIwOLZpzBvbs+UrZ7h5en69J1fiqGl0vfV5cbDW989orPVSfzs26vqc7ejHBL\nNsD9ioTi+0pnb8bVlAsw9Rrze9/S5UG+ElVEYAUwZehlTl0KP7l9cWyKfodN5e4dXkcFVA8vF7+v\nLjcV3vjcczI0DLi7pja/elT6b3abRgDiBzXzbyszpy6Fkdy45TXm90FQpwf5SpP4wCrK3BvJlS8P\nCYMuQ9J2VO3e4XdUIOk3Br/fz2tvN869ZCfF7AF315SstwrA8/lrtVa3NlWNn9y+ePLnREFZxd8n\nLg/ySZT4wKrDzdm8UMLczNtJe6wuXD+7d6i6Yau4Mfi9SQUZhPx8P6+93ST0ku2K2RuQB0RZhq7V\nZ8lYHUurv2HxcpzS91f594nLg3wSJT6wRv3UVnqhFIDJ4Fq8PnTZ1u5QehBB3lhVD7P6vTH4/a5B\nByE/38/rA6OKB01deryyYvbfveFSYXtkf8+Z06oxdL68dzmnLiX83OIH5VLmsZT9bdP1tYH/fUy6\n5JZUIttawXEXde1U0YViBlVzTeiDrxxB5rOMR1Gt1KDbo1Nt0uK6sMPnx5CqMqb8u5sbg9/vGvSx\nal+5CLWp6imvOf1+smFQ83VZfV2/D5pmcArrfLVSXDcaAKoNAwUAe48NCNsj+3umqqsmlpsVSVUb\nk8O1xYq/v8yHg1nPf1vVSYCsqx2NxPdYo35qs7tQwh6qjroHb6W0R3FqOIdUtYH62pRwjaMdv981\n6GPlZ/i82jAml5iUvm7V0/Y7CqDD1EoxN0lusr/b6WwOT6291tHfwa7OMTBxLN38bYtHAKokf1c/\nSYAMpOFLfGCNeomF3Y3M6c1b1fCbzvMuoptWLl/AzOk1OPSTFZLfkvP7XcM4Vl5vfKKbr/m6VfDz\n+6AZxoNZUBWQrP6eTv8Odt+z+Fg6ec/ShyDR35XDt/GT+KFg4MIWTe9uXYU3OlpDfYKzGxJyMlSt\ncvjNz/Bj0FTftP1+V52PlWy7xHR9reVx9Ds8GPTUipdz3el5o+LvafU9vQy1ynrA1YbB4dsYS3yP\nNWp2PWYnPQiVw29R9+CtBLUW1ut31flYWZ03xZuIFzOPo5/hQTc9Xi+jLF7OdafnjYq/p+z7ew1+\nsoeC8UIB725d5fr9gqRL0locMLCGwOpG5uRiV92T03XeJYj5cL/fVbdjVXxzq69LYXpN1ZT5ZwAY\nOl9ekjJVpWaPYqfByU1GdfF3kpUszAxm0dmbEf4t3Jw3Ks4HQN3Dls5TM8WSsEwrTAysGrC72IO6\n+ERPoIsi3N5R5x6iDkTJXbWpajy19topJf9y+fLwNGtGjbLj6CQ4Oe15dvefxS8PvGebEARAeiMP\n+7xR+bAVdXKlU7olremOgTUGgrj4ZE+gf3PDXES5xaNuPUSdOLm5yUYxBofl1YWC4HSUZfvBU46C\nKmC/w1Icz5u4PEzqvJpARwysMRDExSe7SW8/eAo/0mtqhz7j5Oamy9Ci03YMSHZSkrEaEo6rODwU\n6HJexUVFZAUngerMZtlN2u2NjsLjJCNXl0xmp+1omCl+tq82DOHrACIrSFHJdDmv4oKBtULJbtKy\nGx1Fz8nNTZdqO07bse66OcLv9J3rLyl73aRTpTAVZFWydKLLeRUXvItWKNm87brr5kTYKrLidEpA\nl6FFJ+1oXTgb6QVp4Xf6ymVzcf+OQ8LfS8rcnups2yCXxOhyXsUBA2uFkt2kF804E3HLyEoSb26y\n79TWkpYWu0/K3J7KbFtRkN6w4xD+471P8Xhbs7I2iz5X9+SrsDGwVjDRDa2vj4GV9OEkIz7ON3aV\n2bayDT9+feA4vnLZ3ECOCde3inGOlYi0ZTe3p9NuO16oLBEpC8YFILA5ad13y4oKe6xEpAVZz9Nq\n+NvJUGrYPVo3n6dyjbpsSQwQ3Jw017eKscdKRJHz2vO0u7GH3aN1+3kqs23bVy6CbJFSUHPSUe93\nrSsGViKKnNchRbsbe9hDlV4+T9Ua9baWNL57w6VlwTXI9aZc3yrGwEpEkbPqeVqt87S7sYc5VNnZ\nmwl9KLbU423NeGrttaGtN+X6VjHOsRJR5GTzgxfXpiyzTu3W9oZVis8cApYJc2g07CVZSVwC5hcD\nKxFFTpbEYxiwTU6yurEHtXuMmaCUGcyi2jCQL8g2vOPQaCViYCVKuDis85T1PDf4rLwUxAYWpWs3\nrYIqAA6NViAGVqIEi9MCflHPU0XlJdVDlaIEJZl0fa12x5mCx+QlogSL+wJ+HbNO3SQiDY2OxaZY\nBanDwEqUYHFfwK9j1qmb3vJgNherSlCkBoeCNRCHOTCKpyRsUK1b1qkoIcpkYKKEYDGvRfUpvthj\njVjca52S3nQcSo274l40cGFT9nR9bVlQNcVlhIDUYI81Yiq3jSIqFURWLJX3os1RJ5k4jRCQfwys\nEYv7HFgcVdrQu25DqUlTmnldiiMElYeBNWJJmAPzKooAF6flJxQPVstv0hXw4EblOMcasUqdA4tq\nbjnuy09IP7LRJQPwVVSf4ouBNWI6LicIQ1QBjkPv8WVVjD9K3DqNSnEoWAOVOAcWVYCr5KH3OAtj\nCN/r1ERQ9YgpvthjpUhE9ZRfqUPvcRf0CIefqQmno0669rhJPfZYNVQJWatRPeVz+Uk8BT3C4XfZ\nm92oE5PmKgsDq2Yq5QKMMsBV4tB73AU9hK974KZ4YWDVTCVdgAxw5FTQIxxxD9ykF86xaoYXIFG5\noLPng557Z+ZwZWGPVTPMWiUSC3KEI+ipCWYOVxYGVs3wAiSKhtvA7SbJkElzlYWBVTO8AIn05yXJ\nkDkFlYOBVUO8AIn0VklJhuQek5eIiFxikiFZYWAlInKJWb5khYGViMgllsYkK5xjJSJyiUmGZMVR\nYN23bx+eeOIJjI+P46677sIPfvCDoNtFRKQ1JhmSjO1QcD6fx09/+lM8++yz6Orqwu7du/HHP/4x\njLYRERHFjm1gffvtt3HZZZfhkksuwbRp07Bq1Srs2bMnjLYRERHFju1Q8IkTJ9DY2Dj53/Pnz8fb\nb78daKOSpBK2gCOi4PAeEj+2gbVQKJS9ZhhG2Wt9fX1qWqTAyMiIFu3p7j+Lp/d/gtH8xDHMDGbx\nP3ceRubDDFoXzo64dWK6HLu44XHzhsfNmtU95GsLUjx2HoRxztkG1sbGRnz88ceT/33ixAnMmzev\n7OeamprUtsyHvr4+Ldpz767uyQvCNJov4IUj5/CjVV+NqFXWdDl2ccPj5g2PmzWre0jrwi/w2Hmg\n6pzr6emR/pvtHGtzczP+9Kc/4f3338f58+fR1dWF1tZW342qBKzOQkR+8B4ST7Y91pqaGjz66KO4\n9957kc/nsWbNGnz5y18Oo22xxy3giOJB13lM3kPiydE61ptvvhk333xz0G1JHG4BR6Q/LzvVhMX6\nHnImuoaRJZY0DFBbSxpbVjcjXV8LA0C6vhZbVjdHfrES0QVWO9VEjfeQeGJJw4CxOguR3nSfx+Q9\nJH4YWImoosVlHrN0Hvju5llgUrCeOBRMRBUtDjvVmPPAmcEsCpiYB356/yfo7M1E3TQSYGAloooW\nh3lM0TzwaL6gxTwwleNQMBFVPN3nMXWfB6ap2GMlItKcbL5Xt3lgmsDASkSkOdE88PRqQ6t5YLqA\nQ8FEFApRdaNFM6JuVTyYw9SlWcE6D19XMgZWIgqcrLrR39wwV7slI7qWNyydB+bONvriUDARBU5W\n3Wj7wVMRtUhMtKzlwVeOcFkLucLASkSBk2WvDgyNhdwSazqXN6T4YGAlosDJslcbZuo1G8VlLaQC\nAysRBU5W3WjddXMiapEYl7WQCgysRBQ4WXWj1oWzo27aFHEob0j602schogSS1TdqK9Prz1FRcta\ndMkKpvhgYCUiKqJ7eUPSH4eCiYiIFGJgJSIiUoiBlYiISCHOsRIRuaRr2UPSAwMrEZELsrrHABhc\nCQCHgomIXGHZQ7LDwEpE5ALLHpIdBlYiIhdY9pDsMLASEbnAsodkh8lLREQusOwh2WFgJSJyiWUP\nyQqHgomIiBRiYCUiIlKIgZWIiEghBlYiIiKFGFiJiIgUYmAlIiJSiIGViIhIIQZWIiIihRhYiYiI\nFGJgJSIiUsgoFAoFv2/S09Ojoi1ERESxsXTpUuHrSgIrERERTeBQMBERkUIMrERERAolLrDu27cP\nK1euxF//9V/jmWeeibo5sfDRRx/he9/7Hm699VasWrUK27dvj7pJsZLP59HW1oYf/vCHUTclVs6c\nOYP169fjlltuwa233ore3t6omxQLzz33HFatWoXbbrsNGzduxOjoaNRN0taDDz6IG2+8Ebfddtvk\na4ODg7jnnnuwYsUK3HPPPTh9+rTyz01UYM3n8/jpT3+KZ599Fl1dXdi9ezf++Mc/Rt0s7VVXV6Oj\nowO/+c1vsGPHDrzwwgs8bi48//zzuOKKK6JuRuw88cQT+PrXv45//ud/xq5du3gMHThx4gSef/55\nvPzyy9i9ezfy+Ty6urqibpa2Vq9ejWeffXbKa8888wxuvPFG/Mu//AtuvPHGQDpgiQqsb7/9Ni67\n7DJccsklmDZtGlatWoU9e/ZE3SztzZs3D4sXLwYAzJo1CwsXLsSJEyciblU8fPzxx/jtb3+LO++8\nM+qmxMq5c+fw1ltvTR63adOm4aKLLoq4VfGQz+cxMjKCsbExjIyMYN68eVE3SVt/8Rd/gYsvvnjK\na3v27EFbWxsAoK2tDf/6r/+q/HMTFVhPnDiBxsbGyf+eP38+A4RLH3zwAfr6+rBkyZKomxILTz75\nJNrb21FVlahLKXDvv/8+5s6diwcffBBtbW14+OGHMTw8HHWztDd//nx8//vfx/Lly3HTTTdh1qxZ\nuOmmm6JuVqz8+c9/nnwYmTdvHj799FPln5Gou4Fo5ZBhGBG0JJ6Ghoawfv16PPTQQ5g1a1bUzdHe\n3r17MXfuXFxzzTVRNyV2xsbG8Ic//AHf+c530NnZidraWuZEOHD69Gns2bMHe/bswb//+78jm81i\n165dUTeLSiQqsDY2NuLjjz+e/O8TJ05wmMShXC6H9evX4/bbb8eKFSuibk4sHDx4EN3d3WhtbcXG\njRtx4MABPPDAA1E3KxYaGxvR2Ng4OTJyyy234A9/+EPErdLf/v378cUvfhFz585FKpXCihUrmPTl\n0uc+9zmcPHkSAHDy5EnMnTtX+WckKrA2NzfjT3/6E95//32cP38eXV1daG1tjbpZ2isUCnj44Yex\ncOFC3HPPPVE3JzY2bdqEffv2obu7Gz//+c9xww034Gc/+1nUzYqFhoYGNDY2or+/HwDw5ptvMnnJ\ngQULFuDw4cPIZrMoFAo8bh60trais7MTANDZ2Ym/+qu/Uv4ZNcrfMUI1NTV49NFHce+99yKfz2PN\nmjX48pe/HHWztNfT04Ndu3bhqquuwh133AEA2LhxI26++eaIW0ZJ9sgjj+CBBx5ALpfDJZdcgi1b\ntkTdJO0tWbIEK1euxLe+9S3U1NSgqakJa9eujbpZ2tq4cSN+//vf49SpU/jLv/xL/PjHP8YPfvAD\n3H///di5cye+8IUv4O///u+Vfy5LGhIRESmUqKFgIiKiqDGwEhERKcTASkREpBADKxERkUIMrERE\nRAoxsBIRESnEwEpERKQQAysREZFC/x/KRd8BaKrHOAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fc9c3c82790>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X = numpy.concatenate([numpy.random.normal((7, 2), 1, size=(100, 2)),\n",
    "                       numpy.random.normal((2, 3), 1, size=(150, 2)),\n",
    "                       numpy.random.normal((7, 7), 1, size=(100, 2))])\n",
    "\n",
    "plt.figure(figsize=(8, 6))\n",
    "plt.scatter(X[:,0], X[:,1])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It seems clear to us that this data is composed of three blobs. Accordingly, rather than trying to find some complex single distribution that can describe this data, we can describe it as a mixture of three Gaussian distributions. In the same way that we could initialize a basic distribution using the `from_samples` method, we can initialize a mixture model using it, additionally passing in the type(s) of distribution(s) to use and the number of components."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "model = GeneralMixtureModel.from_samples(MultivariateGaussianDistribution, 3, X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can look at the probability densities if we had used a single Gaussian distribution versus using this mixture of three Gaussian models."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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SMCMkWAiCKFdE12jW42iMVXaRJSmZULEoAZNkGTVtq7GgLGRYFLMsCyv7MptG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\nkFghCIIgCIIgCKIo+f8BMinxqmFftzUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fc9c20c9f90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = numpy.arange(-1, 10.1, .1)\n",
    "y = numpy.arange(-1, 10.1, .1)\n",
    "\n",
    "xx, yy = numpy.meshgrid(x, y)\n",
    "x_ = numpy.array(list(zip(xx.flatten(), yy.flatten())))\n",
    "\n",
    "p1 = MultivariateGaussianDistribution.from_samples(X).probability(x_).reshape(len(x), len(y))\n",
    "p2 = model.probability(x_).reshape(len(x), len(y))\n",
    "\n",
    "\n",
    "plt.figure(figsize=(14, 6))\n",
    "plt.subplot(121)\n",
    "plt.contourf(xx, yy, p1, cmap='Blues', alpha=0.8)\n",
    "plt.scatter(X[:,0], X[:,1])\n",
    "\n",
    "plt.subplot(122)\n",
    "plt.contourf(xx, yy, p2, cmap='Blues', alpha=0.8)\n",
    "plt.scatter(X[:,0], X[:,1])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It looks like, unsurprisingly, the mixture model is able to better capture the structure of the data. The single model is so bad that the region of highest density (the darkest blue ellipse) has very few real points in it. In contrast, the darkest regions in the mixture densities correspond to where there are the most points in the clusters."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### A more complex example: independent component mixture models"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Most data is more complex than the Gaussian case above. A common case in the domain of signal processing is analyzing segments of steady signal based on the mean, noise, and duration of each segment. Let's say that we have a signal like the following which is made up of long low-noise signals and shorter high-noise signals."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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N7EyJIQDgRlyOsYtAiEnYcuUF3vojQuH79FRVtzglPHgvOod7SRy57z96VYD4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\nERERERGRGQyaiIiIiIiIzPh/DA3O2fXHLucAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fc9c1936b90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mu = numpy.random.normal(7, 1, size=250)\n",
    "\n",
    "std = numpy.random.lognormal(-2.0, 0.4, size=250)\n",
    "std[::2] += 0.3\n",
    "\n",
    "dur = numpy.random.exponential(250, size=250)\n",
    "dur[::2] -= 140\n",
    "dur = numpy.abs(dur)\n",
    "\n",
    "data = numpy.concatenate([numpy.random.normal(mu_, std_, int(t)) for mu_, std_, t in zip(mu, std, dur)])\n",
    "\n",
    "plt.figure(figsize=(14, 4))\n",
    "plt.title(\"Randomly Generated Signal\", fontsize=16)\n",
    "plt.plot(data)\n",
    "plt.xlabel(\"Time\", fontsize=14)\n",
    "plt.ylabel(\"Signal\", fontsize=14)\n",
    "plt.xlim(0, 10000)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can show the distribution of segment properties to highlight the differences."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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yxGHBANQcH374oXr16mVz/ZAhQ+Tl5aX+/furf3/bH9SvygRbzXJzylxfVFik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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fc9c1cfa210>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(14, 4))\n",
    "plt.subplot(131)\n",
    "plt.title(\"Segment Means\", fontsize=14)\n",
    "plt.hist(mu[::2], bins=20, alpha=0.7)\n",
    "plt.hist(mu[1::2], bins=20, alpha=0.7)\n",
    "\n",
    "plt.subplot(132)\n",
    "plt.title(\"Segment STDs\", fontsize=14)\n",
    "plt.hist(std[::2], bins=20, alpha=0.7)\n",
    "plt.hist(std[1::2], bins=20, alpha=0.7)\n",
    "\n",
    "plt.subplot(133)\n",
    "plt.title(\"Segment Durations\", fontsize=14)\n",
    "plt.hist(dur[::2], bins=numpy.arange(0, 1000, 25), alpha=0.7)\n",
    "plt.hist(dur[1::2], bins=numpy.arange(0, 1000, 25), alpha=0.7)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this situation, it looks like the segment noise is going to be the feature with the most difference between the learned distributions. Let's use pomegranate to learn this mixture, modeling each feature with an appropriate distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{\n",
       "    \"weights\" : [\n",
       "        0.5126040711398554,\n",
       "        0.4873959288601447\n",
       "    ],\n",
       "    \"distributions\" : [\n",
       "        {\n",
       "            \"frozen\" : false,\n",
       "            \"class\" : \"Distribution\",\n",
       "            \"parameters\" : [\n",
       "                [\n",
       "                    {\n",
       "                        \"frozen\" : false,\n",
       "                        \"class\" : \"Distribution\",\n",
       "                        \"parameters\" : [\n",
       "                            6.987501980099923,\n",
       "                            0.9214383552866655\n",
       "                        ],\n",
       "                        \"name\" : \"NormalDistribution\"\n",
       "                    },\n",
       "                    {\n",
       "                        \"frozen\" : false,\n",
       "                        \"class\" : \"Distribution\",\n",
       "                        \"parameters\" : [\n",
       "                            -0.8201943718176836,\n",
       "                            0.13668606405233233\n",
       "                        ],\n",
       "                        \"name\" : \"LogNormalDistribution\"\n",
       "                    },\n",
       "                    {\n",
       "                        \"frozen\" : false,\n",
       "                        \"class\" : \"Distribution\",\n",
       "                        \"parameters\" : [\n",
       "                            0.0055513741389845135\n",
       "                        ],\n",
       "                        \"name\" : \"ExponentialDistribution\"\n",
       "                    }\n",
       "                ],\n",
       "                [\n",
       "                    1.0,\n",
       "                    1.0,\n",
       "                    1.0\n",
       "                ]\n",
       "            ],\n",
       "            \"name\" : \"IndependentComponentsDistribution\"\n",
       "        },\n",
       "        {\n",
       "            \"frozen\" : false,\n",
       "            \"class\" : \"Distribution\",\n",
       "            \"parameters\" : [\n",
       "                [\n",
       "                    {\n",
       "                        \"frozen\" : false,\n",
       "                        \"class\" : \"Distribution\",\n",
       "                        \"parameters\" : [\n",
       "                            7.01255052332367,\n",
       "                            0.9030007437921286\n",
       "                        ],\n",
       "                        \"name\" : \"NormalDistribution\"\n",
       "                    },\n",
       "                    {\n",
       "                        \"frozen\" : false,\n",
       "                        \"class\" : \"Distribution\",\n",
       "                        \"parameters\" : [\n",
       "                            -1.9984343269872586,\n",
       "                            0.37492907121195773\n",
       "                        ],\n",
       "                        \"name\" : \"LogNormalDistribution\"\n",
       "                    },\n",
       "                    {\n",
       "                        \"frozen\" : false,\n",
       "                        \"class\" : \"Distribution\",\n",
       "                        \"parameters\" : [\n",
       "                            0.003718687576817513\n",
       "                        ],\n",
       "                        \"name\" : \"ExponentialDistribution\"\n",
       "                    }\n",
       "                ],\n",
       "                [\n",
       "                    1.0,\n",
       "                    1.0,\n",
       "                    1.0\n",
       "                ]\n",
       "            ],\n",
       "            \"name\" : \"IndependentComponentsDistribution\"\n",
       "        }\n",
       "    ],\n",
       "    \"class\" : \"GeneralMixtureModel\"\n",
       "}"
      ]
     },
     "execution_count": 113,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = numpy.array([mu, std, dur]).T.copy()\n",
    "\n",
    "model = GeneralMixtureModel.from_samples([NormalDistribution, LogNormalDistribution, ExponentialDistribution], 2, X)\n",
    "model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It looks like the model is easily able to fit the differences that we observed in the data. The durations of the two components are similar, the means are almost identical to each other, but it's the noise that's the most different between the two."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The API\n",
    "\n",
    "### Initialization\n",
    "\n",
    "The API for general mixture models is similar to that of the rest of pomegranate. The model can be initialized either through passing in some pre-initialized distributions or by calling `from_samples` on a data set, specifying the types of distributions you'd like. \n",
    "\n",
    "You can simply pass in some distributions to initialize the mixture."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 152,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "model = GeneralMixtureModel([NormalDistribution(4, 1), NormalDistribution(7, 1)])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There is no reason these distributions have to be the same type. You can create a non-homogenous mixture by passing in different types of distributions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 153,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "model2 = GeneralMixtureModel([NormalDistribution(5, 1), ExponentialDistribution(0.3)])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "They will produce very different probability distributions, but both work as a mixture."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 154,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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o0CAsXrwY9+/fR0hICBYvXox33nkHr776KoBnja6RI0fiypUrAIDCwkL89ttvCA0NRUpK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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fc9c131dc10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = numpy.arange(0, 10.01, 0.05)\n",
    "\n",
    "plt.figure(figsize=(14, 3))\n",
    "plt.subplot(121)\n",
    "plt.title(\"~Norm(4, 1) + ~Norm(7, 1)\", fontsize=14)\n",
    "plt.ylabel(\"Probability Density\", fontsize=14)\n",
    "plt.fill_between(x, 0, model.probability(x))\n",
    "plt.ylim(0, 0.25)\n",
    "\n",
    "plt.subplot(122)\n",
    "plt.title(\"~Norm(5, 1) + ~Exp(0.3)\", fontsize=14)\n",
    "plt.ylabel(\"Probability Density\", fontsize=14)\n",
    "plt.fill_between(x, 0, model2.probability(x))\n",
    "plt.ylim(0, 0.25)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "pomegranate offers a lot of flexibility when it comes to making mixtures directly from data. The normal option is just to specify the type of distribution, the number of components, and then pass in the data. Make sure that if you're making 1 dimensional data that you're still passing in a matrix whose second dimension is just set to 1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 159,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X = numpy.random.normal(3, 1, size=(200, 1))\n",
    "X[::2] += 3\n",
    "\n",
    "model = GeneralMixtureModel.from_samples(NormalDistribution, 2, X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can take a quick look at what it looks like:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 160,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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7d08TGYkGpRdWIexe68YEEOMUQw+qDR7rAvF3MXj//fcxceJE3LhxAxs2bEBs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\nVPr/fuN4MK2oIsMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fc9c19f8c90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(6, 3))\n",
    "plt.title(\"Learned Model\", fontsize=14)\n",
    "plt.ylabel(\"Probability Density\", fontsize=14)\n",
    "plt.fill_between(x, 0, model.probability(x))\n",
    "plt.ylim(0, 0.25)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "However, we can also fit a non-homogenous mixture by passing in a list of univariate distributions to be fit to univariate data. Let's try to fit to data of which some of it is normally distributed and some is exponentially distributed. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X = numpy.concatenate([numpy.random.normal(5, 1, size=(200, 1)), numpy.random.exponential(1, size=(50, 1))])\n",
    "\n",
    "model = GeneralMixtureModel.from_samples([NormalDistribution, ExponentialDistribution], 2, X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 148,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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TriOoPaFIrJLzEkuruk6MyLR8rmMQ0ixWhaC4uFgyk1iHDh3w8uVLAMDo0aNV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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fc9c1538e10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = numpy.arange(0, 12.01, 0.01)\n",
    "\n",
    "plt.figure(figsize=(6, 3))\n",
    "plt.title(\"Learned Model\", fontsize=14)\n",
    "plt.ylabel(\"Probability Density\", fontsize=14)\n",
    "plt.fill_between(x, 0, model.probability(x))\n",
    "plt.ylim(0, 0.5)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It looks like the mixture is capturing the distribution fairly well.\n",
    "\n",
    "Next, if we want to make a mixture model that describes each feature using a different distribution, we can pass in a list of distributions---one or each feature---and it'll use that distribution to model the corresponding feature. For example, in the example below, the first feature will be modeled using a normal distribution, the second feature will be modeled using a log normal distribution, and the last feature will be modeled using an exponential distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 163,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X = numpy.array([mu, std, dur]).T.copy()\n",
    "\n",
    "model = GeneralMixtureModel.from_samples([NormalDistribution, LogNormalDistribution, ExponentialDistribution], 2, X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is the same command we used in the second example. It creates two components, each of which model the three features respectively with those three distributions. The difference between this and the previous example is that the data here is multivariate and so univariate distributions are assumed to model different distributions.\n",
    "\n",
    "### Prediction\n",
    "\n",
    "Now that we have a mixture model, we can make predictions as to which component it is most likely to fall under. This is similar to the situation in which you predict which cluster a point falls under in k-means clustering. However, one of the benefits of using probabilistic models is that we can get a softer assignment of points based on probability, rather than a hard assignment to clusters for each point. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 179,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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n9TV04njVzIPHyywvA/ekQ9zo+AI3zp+XMTLDVWDWjLzmvpicWMPV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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fc9c1a9dc50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X = numpy.random.normal(5, 1, size=(500, 1))\n",
    "X[::2] += 3\n",
    "\n",
    "x = numpy.arange(0, 10, .01)\n",
    "\n",
    "model = GeneralMixtureModel.from_samples(NormalDistribution, 2, X)\n",
    "\n",
    "plt.figure(figsize=(8, 4))\n",
    "plt.hist(X, bins=50, normed=True)\n",
    "plt.plot(x, model.distributions[0].probability(x), label=\"Distribution 1\")\n",
    "plt.plot(x, model.distributions[1].probability(x), label=\"Distribution 2\")\n",
    "plt.plot(x, model.probability(x), label=\"Mixture\")\n",
    "plt.legend(fontsize=14, loc=2)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The prediction task is identifying, for each point, whether it falls under the orange distribution or the green distribution. This is done using Bayes' rule, where the probability of each sample under each component is divided by the probability of the sample under all components of the mixture. The posterior probability of a sample belonging to component $i$ out of $k$ components is\n",
    "\n",
    "\\begin{equation}\n",
    "P(M_{i}|D) = \\frac{P(D|M_{i})P(M_{i})}{\\sum\\limits_{i=1}^{k} P(D|M_{i})P(M_{i})}\n",
    "\\end{equation}\n",
    "\n",
    "where $D$ is the data, $M_{i}$ is the component of the model (such as the green or orange distributions), $P(D|M_{i}$ is the likelihood calculated by the `probability` function, $P(M_{i})$ is the prior probability of each component, stored under the `weights` attribute of the model, and $P(M_{i}|D)$ is the posterior probability that sums to 1 over all components.\n",
    "\n",
    "We can calculate these posterior probabilites using the `predict_proba` method."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 183,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.99969547, 0.00030453],\n",
       "       [0.99849679, 0.00150321],\n",
       "       [0.99284427, 0.00715573],\n",
       "       [0.96765651, 0.03234349],\n",
       "       [0.86944497, 0.13055503],\n",
       "       [0.60478603, 0.39521397],\n",
       "       [0.26632011, 0.73367989],\n",
       "       [0.08163   , 0.91837   ],\n",
       "       [0.02197475, 0.97802525],\n",
       "       [0.00582886, 0.99417114]])"
      ]
     },
     "execution_count": 183,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = numpy.arange(4, 9, 0.5).reshape(10, 1)\n",
    "\n",
    "model.predict_proba(X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we scan from left to right, we can see that the probability of the first component (in orange) decreases, while the probability of the second component increases. This makes sense, because the green component is centered at a higher value. The posterior probability is not the probability of the point given the distribution, but rather the probability of the distribution given the point, i.e., which component is more likely to have generated the distribution. "
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.15"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}
